Advertisement

Stochastic Numerics for Mathematical Physics

  • Grigori N. Milstein
  • Michael V. Tretyakov

Part of the Scientific Computation book series (SCIENTCOMP)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Grigori N. Milstein, Michael V. Tretyakov
    Pages 1-82
  3. Grigori N. Milstein, Michael V. Tretyakov
    Pages 83-170
  4. Grigori N. Milstein, Michael V. Tretyakov
    Pages 171-210
  5. Grigori N. Milstein, Michael V. Tretyakov
    Pages 211-282
  6. Grigori N. Milstein, Michael V. Tretyakov
    Pages 283-338
  7. Grigori N. Milstein, Michael V. Tretyakov
    Pages 339-406
  8. Back Matter
    Pages 541-596

About this book

Introduction

Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. The authors propose many new special schemes, some published here for the first time. In the second part of the book they construct numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

Keywords

Monte Carlo Simulation Potential Problems of Mathematical Physics Stochastic Analysis Stochastic Differential Equations Stochastic Modelling Strong and Weak Approximation for SDE mathematical physics random walk

Authors and affiliations

  • Grigori N. Milstein
    • 1
    • 2
  • Michael V. Tretyakov
    • 3
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Department of MathematicsUral State UniversityEkaterinburgRussia
  3. 3.Department of MathematicsUniversity of LeicesterLeicesterUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-10063-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05930-8
  • Online ISBN 978-3-662-10063-9
  • Series Print ISSN 1434-8322
  • Buy this book on publisher's site